Allow me to take a different tack:
Major John Richardson, K.S.F. writing about the War of 1812, incorporating his own experiences, entitles his 1842 publication:
"Operations of the Right Division of the Army of Upper Canada During the American War of 1812".
Within this work, published 25 years before Confederation, we find numerous places where it is quite clear that the Canadian soldiers were distinguished from British ones, and that the Canadians (both Upper and Lower) had a recognizable national identity even if it was not formally recognized in law.
From his own narrative:
"...than that which records the gallant deeds performed by the Fathers, fighting side by side with the troops of England in defence of their invaded firesides:" (comment: side-by-side infers they were distinct parts of a whole)
Now to be fair his sentiment could reflect a change that occured in the three intervening decades, possibly stemming from the 1820's when the two provinces of Canada were united. Thankfully Richardson transcribes a number of contemporaneous documents, Alexander Clark Casselman when re-publishing Richardson's work in 1902 adds a few more such records, and we also have a large body of official correspondences collated and transcribed by Ernest Cruickshank to draw upon. Among these sources we find:
25 Feb 1812 - Major-General Sir Isaac Brock:
"I had every reason to expect the almost unanimous support of the two branches of the Legislature to every measure Government thought necessary to recommend, but after a short trial found myself egregiously mistaken in my calculations.
The many doubtful characters in the militia made me very anxious to introduce the oath of aligenation [sic] into the bill. There were twenty members present when this highly important measure was lost by the casting voice of the chairman." (Comment: This suggests to me that Militias of the two Canadas may not have even given allegiance (aligenation) to the Crown - if so I would be hard pressed to consider them 'British'.)
17 July 1812 - Captain Charles Roberts, 10th Royal Veterans writes:
"By the exertions of the Canadians one of the guns was brought up to a height commanding the garrison, and ready to act"
22 July 1812 - Major General Sir Isaac Brock's proclamation, issued by Capt. J.B. Glegg, A.D.C. refers to the people of Upper Canada as "Canadian Subjects"
Undated (the events related suggest a date of August 1812) - Major Dalliba, an officer within the 4th U.S. Regiment:
"The courtine was lined with British regular troops... The flank of the courtine, on the enemy's right, and American left was lined with Canadian Militia and Indians, commanded by Walk-in-the Water and Marpot."
9 Aug 1812 - Brigadier-General Hull, Commander of the Army of the Northwest:
"From all the information, a large Indian and Canadian Force may be expected from Mackinack"
10 September 1812 - Colonel Lewis Cass, 3rd Ohio volunteers:
"They had 29 platoons, 12 in a platoon, of men dressed in uniform. Many of these were evidently Canadian Militia."
15 July 1814 - Lieutenant-Colonel Tucker (unit of origin unstated but I believe from other reading he was of the 8th (King's) Regiment):
"The Canadian Militia harrassed the enemy in a very manly and spirited style. They merit my most favorable opinion"
I think between these snippets it is quite clear that the British Commanders distinguished Canadian units from British ones. The fact that the Americans made the same distinctions between the British and Canadian troops they faced suggest to me that this is not a case or 'othering'.